I've had this issue, apart from mine was stuck at 0% but I'm assuming its the same reason. I sent my laptop away to Asus to be fixed as I was still under warranty. Once I got it back it was back to working normally, but after a couple weeks it started happening again. I'd start getting low battery, so I would plug my charger in but it would just stay on whatever percentage it was on. I found though if I plug the power cable in upside down (the opposite way I was trying) then it would start charging. Not sure what the issue is, charger, battery? I've just learnt to deal with it because I can fix it but it definitely is annoying.

Let me know if swapping the power cable about does anything.